To use the Math round questions in Powerpoint format, you must have access to

MathType:

MathType is used to create the math questions. You can download a free 30-day

trial copy of the MathType program at

http://www.dessci.com/en/products/mathtype/trial.asp?src=hpmt

After the 30-day trial period, the program becomes MathType Lite. You can still

use it to project the Powerpoint; you just won’t be able to create any math

equations after the 30 days has expired.

Indiana Academic Super Bowl

A Program of the Indiana Association of School Principals

Mathematics Round2015 – Senior Division Coaches Practice

Students:

Throughout this competition, foreign

names and words may be used.

If there are any discrepancies

between how a word/phrase should

be pronounced and what you see

on the screen, the screen

supersedes what is spoken.

SD-CP-M-1

A central angle of 60° is plotted on a circle

with a radius of 12 inches. Calculate the

area of the circular segment between the

chord joining the ends of the two radii and

its corresponding arc.

A. 13 in2

B. 16.5 in2

C. 21 in2

D. 24.5 in2

SD-CP-M-2

Two circles in the same plane cannot

have the following number of common

tangents:

A. 1

B. 2

C. 3

D. 4

SD-CP-M-3

Solve for x.

A. 6

B. 7

C. 8

D. 9

5x + 1

8.4

x

SD-CP-M-4

A. 24

B. 32

C. 40

D. 48

T

C F

Given ⊙O.   If 𝑚 𝑇𝐶 = 132∘,   find 𝑚∠𝐶𝑇𝐹.

SD-CP-M-5

Triangle ABC is inscribed in a circle. The

measure of the non-overlapping minor arcs

AB, BC, and CA are, respectively, x + 75°,

2x + 25°, and 3x – 22°. Then one interior

angle of the triangle is ___________.

A. 57°

B. 59°

C. 60°

D. 61°

SD-CP-M-6

A circle has a radius of 12 units. What is

the length of a minor arc formed by a

central angle of 120°?

A.4π

B.8π

C.16π

D.24π

SD-CP-M-7

Concentric circles have radii of 4” and

6”. If a central angle cuts off an arc of

4” on the circle with the 4” radius, then

the length of the arc it will cut off on the

circle with a 6” radius is _________.

A. 4”

B. 6”

C. 8”

D. 9”

SD-CP-M-8

Circle I is circumscribed about a given

square and Circle II is inscribed in the given

square. If r is the ratio of the area of Circle I

to that of Circle II, then r equals ________.

A.

B. 2

C.

D. 8

SD-CP-M-9

If the radius of a circle were increased

by 2 inches, the area would be

increased by 32π square inches. What

is the radius?

A.4 inches

B.5 inches

C.6 inches

D.7 inches

SD-CP-M-10

If d is the diameter of a circle, then

πd2 represents _______.

A. the area of the circle

B. half the area of the circle

C. one-fourth the area of the circle

D. four times the area of the circle

SD-CP-M-11

The number of circular pipes with an

inside diameter of 1 inch which will

carry the same amount of water as a

pipe with an inside diameter of 6 inches

is _________.

A. 6π

B. 6

C. 36π

D. 36

SD-CP-M-12

The radii of two circles are in the ratio

2 to 3. If the area of the larger circle is 54π,

find the area of the smaller circle.

A. 6π

B. 18π

C. 24π

D. 36π

SD-CP-M-13

If the circle with center A has an area of

72π, what is the area of the circle with

center B?

A.12π

B.18π

C.24π

D.30π

A B

SD-CP-M-14

Each of the three shaded areas is a semicircle.

If AB = 6, CD = 2BC and BC = 2AB, then the

area of the entire shaded figure is ____.

A. 90π

B.

C.

D. 108π

189𝜋

2

203𝜋

2

ADB

C

SD-CP-M-15

If the area of a circle is 64π, then the

circumference of the circle is _____.

A. 8π

B.16π

C.32π

D.64π

SD-CP-M-16

If the radius of a circle is increased by 1

unit, the ratio of the new circumference

to the new diameter is _______.

A. π + 2

B. π (r + 1)

C. π

D. 2π

SD-CP-M-17

On a coordinate plane, which point would be

in the exterior of the circle with equation

x2 + y2 – 8x – 4y + 11 = 0?

A. (1, 2)

B. (4, 5)

C. (5, 1)

D. (8, 2)

SD-CP-M-18

Given 2x2 + 2y2 – 4x – 10y = 0,

what is the y-coordinate of the

center of this circle?

A. 1

B. 2

C. 2 ½

D. 2 ¾

SD-CP-M-19

Given 3x2 + 3y2 – 6x – 10y = 0,

What is the approximate radius of

this circle?

A. 1.68

B. 1.71

C. 1.76

D. 1.94

SD-CP-M-20

Given 2x2 + 8x + 2y2 – 3y – 1 = 0,

what is the radius of this circle?

A. 2 B.

C. 4 D.

9

4

9

2

SD-CP-M-21

Given 2x2 + 2y2 + 3x + 5y + 4 = 0,

what is the center of this circle?

A. B.

C. D. The figure is

not a circle

−3

4, −5

4

3

8, −5

2

−3

8,5

4

SD-CP-M-22

ABCD is a square with

Which of the following is FALSE?

A.

B.

C.

D.

|𝐴𝐵| = 4.

𝐶𝐷 = 𝐵𝐴

𝐴𝐵 + 𝐵𝐶 = 2(𝐶𝐷

|𝐵𝐶| = 4

|𝐴𝐵 + 𝐵𝐶| = 4 2

SD-CP-M-23

Given A (7, -2) and B (3, -2), find .

A. 3.47

B. 4.00

C. 7.28

D. 10.89

|𝐴𝐵 |

SD-CP-M-24

Find the measure of the angle between

U = (3, -4) and V = (3, 4).

A. 106.3°

B. 111.5°

C. 126.8°

D. 134.4°

SD-CP-M-25

Given A (1, 5), B (4, 6), and

C (2, 8), find the measure of A.

A. 18.4°

B. 26.8°

C. 39.2°

D. 53.1°

∠

SD-CP-M-26

Find the coordinates of the vertices of the

triangle with sides determined by the graphs:

4x + 3y + 1 = 0

4x – 3y – 17 = 0

4x – 9y + 13 = 0

Which of the following is NOT a vertex?

A. (2, -3) B. (-1, 1)

C. (5, 2) D. (8, 5)

SD-CP-M-27

If

then b = __________.

A. 2 B. 3

C. D. -3

5𝑎

4+ 𝑏 =

11

2 and 𝑎 +

𝑏

3= 3,

7

2

SD-CP-M-28

Given y – x2 = 0 and 2x2 + y2 = 8, then which of

the following is NOT a possible value for either x

or y?

A. -2

B. 2

C.

D.

− 2

2

SD-CP-M-29

Given x2 + y2 = 4 and 2x2 + y2 = 5, then

which of the following is NOT a

possible value for either x or y?

A. 0

B. 1

C. -1

D. − 3

SD-CP-M-30

Given x2 + y2 = 9 and 3x2 + y2 = 3, then y =

A.

B.

C

D. There is no solution

3

6

12

SD-CP-M-31

Given x + y + z = 6

2x – y + z = 3

x – y + 2z = 5,

the sum of the solutions is _________.

A. -4

B. 0

C. 3

D. 6

SD-CP-M-32

The graph of x2 + y = 10 and x + y =

10 intersect in two points. The

distance between the two points is

______.

A. 1

B.

C.

D. 2

2

3

SD-CP-M-33

If 2a + 3b = 0 and 5a – 2b = -19, then

a = ___________.

A. -3

B. -5

C. D. 2−57

11

SD-CP-M-34

If 2y = 11 – 3x and 5x = 11 + 4y, then y = ________.

A. -3

B. -1

C. 1

D. 3

SD-CP-M-35

The value(s) of y for which the pair of equations x2 + y2 – 16 = 0 and

x2 – 3y + 12 = 0 may have a real common solution are ______.

A. 4

B. -7, 4

C. 0, 4

D. No y

SD-CP-M-36

Given a system of one straight line and

one parabola, the solution set may NOT

be ____________.

A. One point

B. Two points

C. No points

D. Infinitely many points

SD-CP-M-37

Find the value of k if (-2, 4) is the solution for the system of equations

3x + ky = 18 and 5x + 2 ky = 38.

A. 4

B. 5

C. 6

D. 7

SD-CP-M-38

Given x - y + z = 8

5x + 4y – z = 7

2x + y – 3z = -7

the sum of the solutions is _________.

A. 6

B. 8

C. 8

D. 12

SD-CP-M-39

Given 3x + y = -9 and x – 2y = 4, then x = _____.

A. -3

B. -2

C. 0

D. 1

SD-CP-M-40

Given two linear equations, the solution

set may NOT be __________.

A. No points

B. One point

C. Two points

D. Infinitely many points

SD-CP-M-41

A certain fishing spot is located 45 kilometers

from town. Part of the distance can be driven, but

part of it must be traveled on foot. It if is possible

to drive 19 more kilometers than must be walked,

how far must be walked?

A. 13

B. 16

C. 19

D. 22

SD-CP-M-42

A 30-meter board is cut into two pieces,

one of which is 6 meters shorter than the

other. How long, in meters, is the

shorter piece?

A. 12

B. 14

C. 16

D. 18

SD-CP-M-43

The sum of two numbers is 25 and their

difference is 9. What is the larger

number?

A. 8

B. 11

C. 14

D. 17

SD-CP-M-44

The sum of three numbers is 58. Twice the first

number added to the sum of the second and third

numbers is 71. If the first number is added to four

times the second number and the sum is decreased

by three times the third number, the result is 18.

Which of the following is NOT one of the

numbers?

A. 13

B. 15

C. 20

D. 25

SD-CP-M-45

In the expression of xy2, the value of x and y

are each decreased by 25%. Therefore, the

value of the expression is ______.

A. 50% of the original value

B. 9/16 of the original value

C. 75% of the original value

D. 27/64 of the original value

SD-CP-M-46

Applied to a bill of $10,000, the difference

between a discount of 40% and two

successive discounts of 36% and 4%,

expressed in dollars is _______.

A. $0

B. $72

C. $144

D. $256

SD-CP-M-47

Paul receives a weekly salary of $80 plus a

commission of 2% on sales over $2000 and an

additional 1% of sales over $11,000. If his total

sales were $13,500 for the week, how much did he

earn?

A. $210

B. $315

C. $285

D. $335

SD-CP-M-48

Successive discounts of 10% and 20% are

equivalent to a single discount of _____.

A. 15%

B. 25%

C. 28%

D. 30%

SD-CP-M-49

If a dealer could get his goods for 8% less

while keeping his selling price fixed, his

profit, based on costs, would be increased

to (x + 10)% from his present profit of x%,

which is?

A. 15%

B. 14%

C. 13%

D. 12%

SD-CP-M-50

The ratio of 3 ¼ to 5 ¼ is equivalent to

the ratio of ___________.

A. 3 to 5

B. 5 to 3

C. 13 to 21

D. 5 to 7

SD-CP-M-51

In a local election, votes were cast for Mr.

Dyer, Ms. Frau, and Mr. Borak in the ratio

of 4:3:2. If there were no other candidates

and none of the 1800 voters cast more than

one vote, how many votes did Ms. Frau

receive?

A. 600

B. 650

C. 730

D. 800

SD-CP-M-52

A stock decreases in value by 20%. By what

percent must the stock price increase to

reach its former value?

A. 20%

B. 23%

C. 25%

D. 30%

SD-CP-M-53

Due to inflation, the price of a textbook

increased 5%. The new price is $68.14.

What was the original price?

A. $64.70

B. $64.80

C. $64.90

D. $65.00

SD-CP-M-54

A man bought 10 crates of oranges for a total

cost of $80. If 2 of the crates went bad and

were not sellable, at what price would he have

to sell each of the remaining crates in order to

earn a total profit of 25% of his total cost?

A. $10

B. $12.50

C. $15

D. $17.50

SD-CP-M-55

A chemist wishes to make 9 liters of a 30%

acid solution by mixing 3 solutions of 5%,

20%, and 50%. How much of each solution

must the chemist use if twice as much 50%

solution is used than 5% solution?

A. 1l 5%, 1l 20%, 2l 50%

B. 2l 5%, 3l 20%, 4l 50%

C. 3l 5%, 4l 20%, 6l 50%

D. 4l 5%, 6l 20%, 8l 50%

SD-CP-M-56

If the price of an article is increased by

percent p, then the decrease in percent

of sales must not exceed d in order to

yield the same income. The value of d

is ________.

A. B.

C. D.

1

1 − 𝑝

1

1 + 𝑝

𝑝

𝑝 + 1

𝑝

𝑝 − 1

SD-CP-M-57

Which of the following is not a proper way

to write a Roman numeral?

A. MDCLXVI

B. LXXXVIII

C. DICLXVII

D. DCCXXVV

SD-CP-M-58

A. XCIX

B. C

C. CII

D. CIV

VIII + VIIII • II – IV =

SD-CP-M-59

A. DCCXXII

B. DCCCXVIII

C. DCCCXXXIV

D. DCCCXXVIII

𝐼𝑋𝐷𝐶𝐶𝐶𝐿𝑋𝐼𝑉 ÷ 𝑋𝐼𝐼 =

SD-CP-M-60

LXVII + CCIV =

A. CCLXXI

B. CCLXXXIV

C. CCLXXVI

D. CCLXIX

SD-CP-M-61

Find the mean of 2115, 1E12, and

408.

A. 1215

B. 448

C. 2E12

D. 37

SD-CP-M-62

Find

A. 1335

B. 618

C. XLV

D. 3E12

𝑀𝑀𝐶𝐶𝐼𝑋

SD-CP-M-63

A.

B. 1131315

C. 101138

D. 24E712

𝑋𝐶𝑉𝐼𝐼 • 3712 ≠

𝐼𝑉𝐶𝐿𝑋𝑋𝐼

SD-CP-M-64

If 21812 = 4x48, find the value of

x.

A. 0

B. 2

C. 4

D. 6

SD-CP-M-65

A. CCLXXII

B. 3748

C. 18X12

D. 22045

XXVIII • IX =

SD-CP-M-66

3712 – 2 • 42 + 1612 ≠

A. 1045

B. 338

C. 2512

D. XXIX

SD-CP-M-67

If 31a8 = 14X12, find the value of a.

A. 2

B. 4

C. 6

D. Cannot be determined

SD-CP-M-68

A bar placed on top of a digit in a

Roman numeral increases the

number by a factor of _________.

A. 10

B. 100

C. 1,000

D. 10,000

SD-CP-M-69

The number 10! (in base 10) when

written in base 12 ends with

exactly how many zeroes?

A. 2

B. 3

C. 4

D. 5

SD-CP-M-70

A. 12415

B. 12335

C. 13035

D. 13015

1015 + 125 • 335 − 245 =

SD-CP-M-71

Which mathematician gave birth to the calculus

of the infinite conceived and brought to perfection

by Kepler, Cavalieri, Fermat, Leibniz, and

Newton?

A. Archimedes

B. Heron

C. Pappus

D. Ptolemy

SD-CP-M-72

Which mathematician, considered by

most to be the greatest mathematician of

antiquity, used the method of exhaustion

to calculate the area under the arc of a

parabola?

A.Archimedes

B. Heron

C. Ptolemy

D.Menelaus

SD-CP-M-73

Which mathematician wrote The

Geography, an attempt to summarize

the geographical knowledge of the

habitable world as known at that time?

A. Archimedes

B. Heron

C. Pappus

D. Ptolemy

SD-CP-M-74

Who wrote the Almagest, the

supreme authority on astronomy

until Copernicus’s publications?

A. Archimedes

B. Heron

C. Pappus

D. Ptolemy

SD-CP-M-75

Which mathematician extended and

generalized the Pythagorean theorem,

applying it to all triangles, whether right

triangles or not?

A. Archimedes

B. Pappus

C. Menelaus

D. Heron

SD-CP-M-76

Which mathematician is a key figure

in the development of trigonometry?

A. Archimedes

B. Heron

C. Menelaus

D. Pappus

SD-CP-M-77

Which of the following mathematicians

was not a member of the Museum in

Alexandria, where the study of

mathematics flourished with remarkable

success?

A. Archimedes

B. Pappus

C. Ptolemy

D. Menelaus

SD-CP-M-78

Which mathematician developed a

formula for finding the area of a triangle

from its side lengths?

A. Archimedes

B. Heron

C. Pappus

D. Ptolemy

End of Math Round

Senior Super Bowl Area Contest - April 21, 2015

SD Math Coaches Practice Answer Key:

1. A

2. A

3. A

4. A

5. D

6. B

7. B

8. B

9. D

10. D

11. D

12. C

13. B

14. B

15. B

16. C

17. D

18. C

19. D

20. B

21. A

22. B

23. B

24. A

25. D

26. C

27. B

28. A

29. A

30. D

31. D

32. B

33. A

34. C

35. A

36. D

37. C

38. A

39. B

40. C

41. A

42. A

43. D

44. B

45. D

46. C

47. D

48. C

49. A

50. C

51. A

52. C

53. C

54. B

55. B

56. D

57. C

58. C

59. A

60. A

61. D

62. D

63. B

64. D

65. B

66. B

67. A

68. C

69. C

70. D

71. A

72. A

73. D

74. D

75. B

76. C

77. D

78. B